Fourier Transforms

[T.D. Flint]

Dear Whoever,
I just can not understand exactly what is going on in a Fourier transform.  I 
know that amplitude and phase values are calculated etc and that you end up 
with the power spec. but i have asked SO MANY people what is going on and 
either they don't understand it themselves, or they do and can not explain it 
in such a way for me to understand.  Can any body explain it or give me  a 
reference that is understandable.  I have read many but never quite seem to 
get there.
Thanks
   B
   Y
   E
Toby